Final answer:
In a retail store inventory system, the rational numbers represent profits and losses against a benchmark level, and the inequality -7 < x <= 6.75 defines the acceptable range of profitability, with x representing profit/loss.
Step-by-step explanation:
A real-world situation for the given rational numbers could be an inventory system at a retail store where the variable x represents the profit or loss on sales for particular items in dollars. For example, we could be comparing profits and losses against a benchmark profitability level. Let's define our variable x as the profit or loss on sales of items. The inequality could be written as -7 < x <= 6.75 to represent a boundary for an acceptable range of profitability, where x is constrained to be higher than a certain loss (in this case, -$7) and up to a certain level of profit ($6.75).
Our partial solution set includes 6 3/8 (which represents a profit of $6.375, thus acceptable), -6.25 (represents a loss, but an acceptable loss because it's more than -$7), -31.4 (which is not an acceptable loss, hence not part of the solution), and 6.75 (which is the upper boundary of the acceptable profit and is included in the solution set).
The values are a partial solution set because they represent some of the many possible values for x that satisfy the inequality. Since we are dealing with profits and losses in a store, these numbers are practical estimates that likely arise from real transactions, illustrating the numbers that fit within the store’s financial targets.